Abstract
If $p = 3$ or 5 and $3 \leq n \lt p + 3$, then the homotopy type of $\mathbb{C}P^{n}$ contains only finitely many $PL$ homeomorphism types with a locally linear $PL$ action of the cyclic group of order $p$ fixing an isolated point.
Citation
Robert D. Little. "Periodic mappings of complex projective space with an isolated fixed point." Illinois J. Math. 43 (4) 654 - 671, Winter 1999. https://doi.org/10.1215/ijm/1256060684
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